Despite a long-standing special bilateral relationship, the Italian government has been quietly winding down its once lucrative arms sales to its former North African colony, Libya.

Italian officials reportedly turned down a renewed bid for new arms sales this spring. Libyan Prime Minister Abdul Salaam Jalloud was here to discuss payments problems that have recently clouded flourishing trade and economic relations.

The gradual and largely unpublicized change of policy reflects a souring of political relations in recent years as a result of the policies the Libyan leader, Col. Muammar Qaddafi, has pursued toward Western Europe, Africa and the United States. Although Foreign Ministry officials here are determined to keep a diplomatic dialogue going, concern within the Italian government has grown over what is seen as Libya's excessive military strength. As a result, although old contracts are being allowed to run their course, new arms deals have been blocked.

Italy's Socialist minister of defense, Lelio Lagorio, said in an interview that since taking office in April 1980 he had not authorized any new arms sales to Libya. In an address to the parliament's defense commission last fall, the minister said Libya was "already too strong." He pointed out that it not only has more tanks proportionally than Italy, as well as a technologically superior Air Force, but that it was currently spending 10 percent of its gross national product on defense, more than any Eastern European country.

In recent years, Italy has been a major, although not the largest, supplier of arms to Libya, along with the Soviet Union, France and Britain. The Libyan Army has 100 Oto Melara armored vehicles and 100 Fiat armored personnel and amphibious vehicles, with another 100 reportedly on order.

The Libyan Navy has purchased five corvettes from Cantieri Navali Riuniti and these craft plus others built by the British are armed with Oto Melara missiles and Italian-made Aspide missile launchers.

The Libyan Air Force, made up predominantly of Soviet Migs and French Mirages and Mysteres, has purchased 20 troop transports from Italy as well as several dozen helicopters, and 250 trainers. According to the 1981 World Armaments and Disarmament yearbook, most of these orders were placed in 1978 and 1979.

Foreign Ministry officials were unable to quantify the value of Italian arms sales to Libya, but pointed out that each of the the corvettes cost about $75 million. The current ban on new contracts thus represents a significant commercial loss for Italy, where the major arms manufacturers are totally or partially state-owned. The one consoling factor, said a high-ranking Foreign Ministry official, is that present Libyan financial problems might well have meant cutbacks anyway.

The decision to ban new arms sales reflects a cooling of diplomatic relations between Italy and Libya caused by what a Foreign Ministry official termed "recurrent elements of disturbance" by the Libyan government.

The Italian government was angered by Qaddafi's military threats against Italy following the incidents in the Gulf of Sidra last August--when U.S. carrier jets shot down two Libyan warplanes--and by subsequent death threats against the U.S. ambassador in Rome, Maxwell Rabb. About a dozen Libyans reportedly were expelled from Italy at that time.

U.S. concern about possible Libyan involvement in international terrorism appears to have been taken increasingly into account here.

French representations following Libya's December 1980 invasion of Chad were said to have convinced the Italians to put off indefinitely a long-postponed visit by Qaddafi.

Previously, the 1980 killings here of several of Qaddafi's Libyan opponents had chilled bilateral relations, already clouded by the still unsolved disappearance in September 1978, allegedly on a flight from Tripoli to Rome, of Lebanon's Shiite leader Imam Moussa Sadr.

Despite their concern, however, Italian policy makers have sought to keep open the diplomatic door. Foreign and Defense ministry sources say this reflects the government's conviction that isolation could lead Qaddafi to draw closer to the Soviet Union.

But Western diplomats and many Italian observers say policy makers are also influenced by the encouraging balance sheets of bilateral economic relations as well as by Libya's role as a supplier of crude oil. In recent months, Italian-Libyan trade relations have been clouded by Libyan financial problems that have left that country with debts of $1.15 billion in Italy. But, in general, trade between the two has been thriving.

The Italians moved into Libya in 1911 and reinforced their position there under fascist dictator Benito Mussolini. In 1970, a year after Qaddafi took power, Libya expelled all the Italians then living there. But a rapprochement that began in 1974 led to closer political ties an thriving economic relations.

Libya is Italy's fifth most important trading partner, after West Germany, France, the United States and Britain. It absorbs some 6 percent of Italian exports and, in recent years, has provided Italy with 10 to 14 percent of its imported oil. Some 20,000 Italian workers and technicians are involved in construction products there.

Italy is Libya's main trading partner, supplying 25 percent of its imports. Although precise figures are not available, the Libyans are also believed to have invested heavily in Italian industry and real estate. In 1976, the Libyan National Bank purchased a 9.1 percent share in Fiat and recapitalization is expected to bring it to 13.4 percent by 1983.

In several Italian cities, including Rome, the Libyans appear to have financed small private TV stations where readings from Qaddafi's "Green Book" can sometimes be heard. In Catania, Sicily, the Libyans have financed a mosque and are also believed to own most of the nearby Mediterranean island of Pantelleria.